The residents pronounce it “Ang-will-a.” This immediately sets them apart from most other West Indians and Caribbeanites, who share a French or Spanish ancestry, and thus refer to the island as “Ang-wheel-a.” However, the Anguillans themselves are fiercely proud of their British heritage and status as British citizens, so therefore insist that the name contains a soft “i” sound rather than a hard “e.”

They are also proud of their miles of white sandy beaches (there are 33 on the 35-square-mile island), tropical climate, crystal-clear waters, sports, boating, and the chance to swim with dolphins and dine on lobsters and shrimp. They boast of 360 days a year of sunshine, tons of four-star hotels and restaurants, shopping – in short, everything that most tourists could possibly want. However, beginning last year the Anguillans installed the one thing I personally consider necessary for travel: a jazz festival.

Don’t get me wrong – it’s not that I don’t appreciate tourist attractions. It’s just that if I were ever to visit the Sistine Chapel, I know my first thought would be either, “Hey, that podium would be a great stage for a big band,” or “I wonder how many LPs I could store in here?”

And so, sufficiently motivated, last fall I attended the first Tranquility Jazz Festival – the second takes place on Anguilla this November 10-14 – in spite of the fact that I find the event’s name somewhat off-putting. “Tranquility” suggests to me smooth jazz or New Age or Celtic music. There is every reason to expect to hear such sounds in the Caribbean, since the cable TV music channel BET On Jazz, a co-producer of Tranquility, has lately been promoting and producing musical festivals all over the islands. What makes the Anguilla event special is that unlike the other islands, which generally host a combination of Smooth Jazz and Rhythm and Blues, it features straight-ahead jazz. No elevator-ready “lite,” so-called jazz here, this is the real thing, straight up and swinging.

I booked a room at the Anguilla Great House (www.anguillagreathouse.com, 264-497-6061; $220-$250 a night), a spray of gingerbread cottages along Rendezvous Bay, which was certainly picturesque and comfortable (I especially appreciated the bedside Internet connection), but when I return this year I’m planning to stay at the neighboring Cuisinart Resort & Spa (www.cuisinartresort.com, 264-498-2002; $525-$4,000 a night). Not only is it much bigger and more deluxe, it’s also the host hotel for the festival itself, so will be, I hope, the happening spot.

The 2003 event, coordinated by talent agent and producer Joel Criss, boiled down to two primary nights of full-length jam sessions. The lineup mostly consisted of familiar faces frequently spotted in New York clubs, such as pianist Eric Reed, trombonist Steve Turre, and multireed player Sonny Fortune. I was especially glad to see Donald Harrison and Bobby Watson, a pair of outstanding alto players, both veterans of Art Blakey’s Jazz Messengers, who have made themselves unfortunately scarce in New York of late.

On the first night, pianist Eric Reed’s trio served as the core rhythm section, with bassist Barak Mori and drummer Rodney Green. The opening set was a saxophone summit, starting with Donald Harrison playing John Coltrane’s “Mr. PC.” Bobby Watson then played “Soul Eyes,” a classic ballad by the late Mal Waldron, and imbued it with a Billy Strayhorn feel. The biggest crowd pleaser was, as always, the remarkable James Moody, who, like his mentor, Dizzy Gillespie, is both a great “serious” jazzman and a cut-up of an entertainer incapable of taking anything too seriously. The three saxes then got together on Gillespie’s “Night In Tunisia,” which also seemed especially relevant when situated amongst the palm trees.

The second night also began with Coltrane, and ended with him as well. There was more of a Latin presence, since the stars were pianist Hilton Ruiz, trombonist Steve Turre, flautist Dave Valentine, and percussionist Steve Berrios. With Sonny Fortune on alto and bassist Leon Dorsey, they started with “A Moment’s Notice,” and, with Mr. Ruiz visibly still in charge, then addressed Horace Silver’s “Tokyo Blues.” Vanessa Rubin, a star singer who is generally at her best in all-star presentations such as these, sounded fine on “The More I See You” and even better on “Never Let Me Go.”

Most of the rest of our party, apart from a couple of fellow jazz scribes, consisted of travel writers, so we tagged along with them as they scrutinized the hotels and various other accommodations on the island. The most amazing place to visit is Scilly Cay, a very small island a couple hundred yards out to sea (I swam there from the main island, though free ferry rides are available) that houses an open-air, lunch-only restaurant, also called Scilly Cay (264-497-5123), operated by local heroes Sandra and Eudoxie Wallace. The simple menu – grilled lobster ($50), chicken ($25), crayfish ($50), rum punch ($5 a glass) – is pricey, but worth it. One is taught to resist the temptation to pet the many stray but friendly dogs, who are fed but not housed by the residents, and thus, I am told, often covered with fleas.

On the third and last day I finally got in some good swimming. The waters are so calm and inviting that you can literally swim for miles around the island – I learned the hard way, however, that the only thing you can do to get past a coral reef is to get out and walk around it – do not, I repeat, do not try to swim over it.

I’m looking forward to returning for the second Tranquility Fest, which opens with an al fresco session on Scilly Cay on Wednesday, November 10. The next night, there will be an intimate evening at the Cuisinart with Cyrus Chestnut, one of the most entertaining straight-ahead pianists playing today, in a trio set made even better with swinging vocalist Carla Cook. The next two evenings contrast mainstream jazz and Latin jazz. Friday’s event stars the Mingus Dynasty Sextet, singer songwriter Carmen Lundy, and two outstanding guest alto saxophonists, Gary Bartz and James Spaulding. Saturday is billed as a “Latin Jazz Explosion,” featuring Flora Purim, Airto Moreira, and starring Ray Barretto, the superstar conguerro who has played with virtually everybody and who is turning 75 this year. The festival ends with a beach concert at Sandy Ground on Sunday afternoon.

Arriving back in New York last year, I ran into a West Indian gentleman running the cab stand at JFK. When he asked where I’d been to, I said “Ang-will-a” and he said, “No, it’s pronounced ‘Ang-wheel-a.’ “